I enjoyed tonight's episode of the
Discovery program, Mythbusters, as I do every Sunday, but this
episode was especially interesting because of a segment on a physics
thought experiment called “Blow Your Own Sail”.

This is a very old thought experiment
for physics students. Suppose you are in a sailboat on a day with no
wind, and there is no motor onboard but there is a large fan. Can you
use the fan to blow the sail and propel yourself along?

According to Newtonian physics for
every action there is a reaction, which means that the force applied
on the sail to move the boat forward is exactly cancelled by the
forces on the fan pushing it backwards. Another way to view this is
that since there are no external forces on the boat, the boat cannot
move. Either way, this is a reasonable argument that predicts the
boat will not move.

I happened to work out the mathematics
and physics of this problem many years ago for a school project back
when I was a physics undergraduate student, and so I knew the answer,
but surprisingly many very skilled and experienced physicists use the
false logic above to predict that the boat cannot move. They are
wrong.

The problem with the logic is that it
assumes that the boat is a closed and isolated system. In truth there
are two sources of external forces that most people forget about.

The first and most important is the
recoil of the air after hitting the sail. Air is hard to visualize,
and even harder to handle in Newtonian physics, so I will give a
different example to illustrate this point. Suppose you replace the
fan with a cannon and replace the sail with an indestructable brick
wall. When the cannon is fired, the boat moves backwards from the
recoil. Then the cannon ball hits the wall and the boat's motion
stops. But then the cannon ball bounces off the wall with the same
momentum in the opposite direction and flies off the back of the
boat. Now the system is composed of a boat and a cannon ball flying
backwards from the boat – and by Newton's laws if the cannon ball
is sent out the back with some momentum the boat must react by moving
forward with the same momentum!

The second (and arguably negligible)
effect is a Venturi force created at the front of the boat. An
airplane wing works by creating a low pressure region above the wing,
caused by fast moving air. In the boat and fan experiment, some air
will slip around the edge of the sail and move quickly past it. This
in principle creates a low pressure zone in front of the sail which
sucks the boat along.

There are of course uncertainties in
both of these forces. The problem with the low pressure forces is
that it is very difficult to model, so as far as I know no one has
actually calculated how strong the effect would be. It might have no
effect at all. And with the air recoil forces, there are arguments
that the air being sucked in by the fan counters the air pushed out
backwards – except that the fan increases the energy and momentum
of the air so it doesn't quite balance. There is also an effect of
the sail being flexible and absorbing some of the momentum from the
air – but this is also difficult to model since it depends on the
material used. There are also problems with air being compressible,
with air spilling around the edge of the sail, and with a large
resistance to motion caused by the water beneath the boat.

But the Mythbuster team built it in
full-scale and proved that in fact it is possible with a strong
enough fan and large enough sail to actually power a boat this way.
Really cool experiment!